Shah is an MLA from Naranpura constituency in Ahmedabad city. Being an MLA, he has to get his attendance marked in the Assembly once in six months.
Before meeting Vaghela, who is the opposition leader in the Assembly, the BJP chief attended the session.
Gujarat chief minister Vijay Rupani and state BJP chief Jitu Vaghani were present during the meeting that took place at Vaghela's chambers at the Assembly building.
After the meeting, which lasted for about half an hour, Vaghela termed it as a "courtesy call".
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When asked if there was any indication of advancing the state polls due later this year, Vaghela said, "There were no indications of early polls, as I understand, but nothing can be said of these RSS people."
Vaghani also said it was a courtesy call.
"As our national president was here he wished to meet Vaghela and they met," he said.
Shah also attended the lunch hosted by Assembly speaker Ramanlal Vora for MLAs.
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